House leaders today proposed a $33.8 billion budget for the upcoming fiscal year that boosts funding for higher education and local aid but rejects Governor Deval Patrick’s request for higher spending on early education, one of the governor’s top priorities.

House Speaker Robert A. DeLeo said he would not provide any increase in spending on early education, because he questions whether the governor’s agency that oversees the system is managing its money and caseload efficiently.

Patrick had asked DeLeo to approve an additional $131 million for early education to support higher salaries, professional development, and competitive grants to innovative programs that want to expand.

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But DeLeo said he would instead order an audit of the finances at the Department of Early Education and Care and to set up a $200,000 “compliance office” to make sure the agency is spending its money wisely.

DeLeo said he questioned how the department’s waiting list had jumped from 30,000 to 50,000 over the last few months and why, if there is a long waiting list for services, the department has ended the last two years with a surplus.

“Before we make any further investments, we want to make sure their house is in order,” DeLeo said. If the agency can prove its money is being spent prudently, he said, he would be open to increasing funding for early education later in the year.

Overall, the House budget proposes spending $1 billion less than the $34.8 billion annual budget that Patrick proposed in January. House leaders would increase overall state spending by 3.9 percent, compared to the 6.9 percent increase Patrick wants.

Patrick, House leaders, and Senate leaders, who have yet to release their spending blueprint, must agree on a state budget by July 1, when the new fiscal year begins.

Some of the most contentious areas of disagreement between Patrick and lawmakers have already been aired over the last several weeks, as the governor and legislators fight over tax increases to fund transportation. Patrick has proposed a $1.9 billion tax hike, while House and Senate leaders have pushed for an increase in the range of $500 million.

While that battle continues to play out, DeLeo said higher education is one area where he and Patrick agree.

The House budget, like the governor’s budget, seeks an increase of $110 million for higher education, including an additional $29 million for community colleges and $15 million for state colleges. If approved, the increases would allow the University of Massachusetts system to freeze tuitions and fees at their current level, DeLeo said.

Local aid – which funds teachers, police officers, trash collectors, and other municipal services – would see an increase of $21 million in the House budget.

House leaders also proposed the creation of a $300,000 “bureau of program integrity” to crack down on welfare fraud at the Department of Transitional Assistance.

The state inspector general recently reported that the department could not verify that 5,000 of the 50,000 people receiving welfare benefits valued at about $25 million annually are, in fact, eligible for those benefits.